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Some Applications for Projections

Introduction

Frequently a proper choice of projection, scale, orientation and coordinates is crucial for a map to convey its message quickly and unequivocally, as demonstrated by a few examples.

When a reference is presented, the maps in this section are not scannings or reproductions but rather approximate reconstructions of the original sources (for instance, the original faunal regions map does not use an equal-area projection) for illustration purposes.

Faunal Regions and Global Connections

Polar, star-shaped map
Major Faunal Regions of the World
    Neartic
    Palaearctic
    Ethiopian
    Neotropical
    Oriental
    Australasian
    Oceanic
Faunistic division of the world, modified Maurer projection

For zoological classification purposes, the world is divided in faunal regions.
Here (after Oliver L. Austin and Arthur Singer, Birds of the World, Hamlyn Publ. 1968), a map based on Maurer's star projection presents all lands minus Antarctica. Since climate is a great determinant of faunistic features, most regional borders follow latitudes and are, therefore, roughly concentric in polar-aspect maps.

A land arrangement similar to the previous starlike map is employed in the latest version of Buckminster Fuller's icosahedral projection.  It was used for presenting fiber cable routes and intercontinental network traffic in Thomas B. Allen's The Future is Calling, National Geographic 200(6), December 2001.  The projection choice was appropriate, since connections to Antarctica are negligible and no routing lines had to be broken, even across oceans.

Migration Paths

Human migration according to Out of Africa hypothesis
Possible migration of early human population, according to the "Out of Africa" hypothesis; clipped Mercator map, central meridian 150°E
According to the "Out of Africa" theory, modern man appeared as a single African species nearly 100000 years ago, then spread throughout the world (K.Wong, Is Out of Africa Going Out the Door?, Scientific American 281(2), August 1999). A simple coordinate rotation avoids cutting the migration path between Asia and Alaska.
Conjectured migration paths of early American/Asian populations
Present and fossil teeth suggest several migration waves in the past, when reduced sea levels created bridges between now isolated Japanese and Aleutian islands. Cassini projection.

Some particular migration paths relate populations in eastern Asia which may have later populated Polynesia, northern Asia and the Americas. Dental anthropology (Christy G. Turner II, Teeth and Prehistory in Asia, Scientific American 260 (2), February 1989) provides evidence depending on several genetic factors, not culturally acquired and seldom affected by the environment.

Mapping Puns

Snyder's hourglass-shaped equal-area projection
J.P.Snyder's hourglass-shaped projection.

Sometimes, serious cartographers resort to humor in order to make ideas convincing. For instance, John P. Snyder, a prolific and influential author of books, papers and projections, also created an equal-area projection with absolutely no applicability other than evidencing that areal preservation alone does not make a good projection, as some supporters of Arno Peters's projection apparently believe.

Snyder's whimsical proposal, devised ca. 1945 and informally presented in 1987, is a pseudocylindrical design with zero horizontal scale at the Equator, and extreme vertical stretching to compensate. Reciprocally, it is flat-polar, with infinite horizontal scale at both poles. The resulting map resembles an hourglass, with shape distortion much stronger than in the unrelated Collignon map when drawn with two flat poles.

Colligon's equal-area projection in hourglass form
Collignon's projection in the variant with two flat poles

Martin Gardner mentions a geographer being given an award (1973) in the form of a framed map shaped as a bowtie (a favorite of his) drafted by Waldo Tobler, another prolific author. Gardner does not disclose the projection, but it could be a variation of Tissot's design for local maps, referred to by Tobler in 1974.

Snyder's hourglass-shaped equal-area projection
Tissot's projection for local maps, expanded to the 3rd degree; reference latitude 0°. The map may assume stranger shapes, even intersecting itself for some reference latitudes; definitely this is not a projection for world maps.
Snyder's hourglass-shaped equal-area projection
Tissot's projection, reference latitude 90°S.

Orbital Tracks

Great circle in equidistant cylindrical map Great circle in orthographic map
Part of a great circle in an equidistant cylindrical projection The same curve in an orthographic map

The crash of the Mir space station on the Pacific Ocean attracted a lot of attention. Most media coverage used cylindrical projections to depict the station's last moments following an apparently sinuous curve. Of course, the actual path of a low-orbit object looks much more simple when presented tridimensionally or as an azimuthal orthographic map:

Despite popular conceptions and illustrations, many satellites cruise at relatively low orbits, nearly grazing Earth's top atmosphere: a typical average altitude for Mir and the International Space Station is 390 km, while the Space Shuttle routinely performs orbits below 250 km (geostationary satellites ride much higher, at nearly 36000 km). The example is simplified, since orbiting objects neither follow exactly circular trajectories nor keep constant altitude; besides, the planet itself does not lie still but rotates beneath their paths.

The curve separating day/night areas is also roughly a great circle, thus the sinuous graphics in popular desktop programs displaying a "sun clock" on rectangular maps.

Heavenly Maps

For most of mankind's history, stars and planets were mainly an aid for navigation and time reckoning. In this role, it is perfectly appropriate thinking of heavenly bodies as attached to an enormous spherical shell slowly rotating around Earth. Such a sphere can be mapped by exactly the same processes as used for ordinary maps. In fact, some map projections were first used by early astronomers for charting the skies instead of lands.
Northern (boreal) sky in stereographic projection Southern (austral) sky in stereographic projection
Sky in boreal hemisphere Sky in austral hemisphere sky
Two polar azimuthal stereographic maps present the night sky as seen in the north and south poles. Viewers in other latitudes and dates will see the constellations more or less tilted.
In the boreal (northern) sky map, the Big Dipper appears at the 9 o'clock position, at the second innermost circle. The bright star at 10 o'clock is Arcturus; the Polar star is slightly below the heavenly North pole. In the austral (southern) sky, the two bright stars at 2 o'clock on the second innermost circle belong to Centaurus and point to the Southern Cross, slightly below and to the right; Sirius is the brightest star near the bottom center.

Work in Progress


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Copyright © 2001, 2009 Carlos A. Furuti